Rectification of Brownian particles in ratchet systems in the presence of an unbiased external force has been an intense area of research in the last few decades [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}.
Here, the external oscillatory (unbiased) force can induce directed motion of the diffusing particles, i.e., known as rectification,
in ratchet systems possessing dynamical or spatial symmetry breaking at submicron scales [3]}.
Particularly, the rectification of Brownian particles in ratchet systems has been inspired by the working principles of Brownian motors [13]}, molecular motors [14]}, nanoscale friction [15]}, surface smoothing [16]}, coupled Josephson junctions [17]}, separation of particles [18]}, optical ratchets and directed motion of laser-cooled atoms [19]}, and mass separation and trapping schemes at the microscale [20]}.
Note that the rectification depends on the physical properties of the diffusing particles such as mass, size, shape, etc. [3]}, [13]}.
In order to observe rectification of particles, the ratchet setup requires two basic ingredients [23]};
(i) asymmetry (spatial and/or temporal) in the system itself
to violate the left/right symmetry in the diffusive behavior of the particles, and
(ii) a zero-mean external oscillatory force to break the thermodynamic
equilibrium, which forbids the appearance of directed motion due to the second law of thermodynamics.
Depending on various nonequilibrium situations, several models have been proposed to obtain rectification of particles such as rocking ratchets [24]}, flashing ratchets [25]}, diffusion ratchets [26]}, and correlation ratchets [27]}.
In all these models, the unbiased driving force can break the thermodynamic equilibrium and induces rectification of particles.
The rectification of non-interacting Brownian particles is a well studied problem both experimentally [2]}, [3]} and theoretically [4]}, [5]}, [6]}.
However, the interaction between the particles may further influence the diffusive behavior of particles in confined geometries [33]}.
Usually, the short range interaction force between the Brownian particles
can be considered as
(i) the lubrication interaction [33]}, [35]},
(ii) the harmonic interaction [36]},
(iii) the Lennard-Jones interaction [37]}, and
(iv) the Yukawa interaction [38]}.
